{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Scale-free hypergraph generation\n", "\n", "In this notebook you will:\n", "\n", "- Generate scale-free hypergraphs with controlled degree correlations.\n", "- Compute size-degree distributions and compare layers.\n", "- Visualize interaction-size effects.\n" ], "id": "3f5bd4fd" }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ".. admonition:: Definition\n", "\n", " Scale-free hypergraphs exhibit power-law degree tails across interaction sizes.\n" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ".. admonition:: You will learn\n", "\n", " Create scale-free hypergraphs and analyze degree patterns across sizes.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "- Generate scale-free hypergraphs and compare degree distributions.\n", "- Visualize sample structures and validate model behavior.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup\n" ] }, { "cell_type": "code", "metadata": {}, "execution_count": null, "outputs": [], "source": [ "import matplotlib as mpl\n", "\n", "mpl.rcParams.update({\n", " \"figure.figsize\": (6, 4),\n", " \"figure.dpi\": 120,\n", " \"savefig.dpi\": 150,\n", "})\n" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "import math\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from scipy.stats import spearmanr\n", "\n", "from hypergraphx.generation.scale_free import scale_free_hypergraph" ], "id": "4a88fc03" }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "# -----------------------------\n", "# Helpers\n", "# -----------------------------\n", "def iter_all_edges(hg):\n", " for e in hg.get_edges():\n", " yield tuple(e)\n", "\n", "def edges_of_size(hg, size: int):\n", " edges = hg.get_edges(size=size)\n", " return edges\n", "\n", "def sizes_present(hg):\n", " return sorted(set(hg.get_sizes()))\n", "\n", "def nodes_present(hg):\n", " ns = hg.get_nodes()\n", " return np.array(sorted(map(int, ns)))\n", "\n", "def degree_by_size(hg, size: int, num_nodes: int | None = None):\n", " \"\"\"Size-specific degrees k_i^{(size)} as a numpy array of length num_nodes.\"\"\"\n", " if num_nodes is None:\n", " num_nodes = int(nodes_present(hg).max()) + 1\n", " deg = np.zeros(num_nodes, dtype=int)\n", " for e in edges_of_size(hg, size):\n", " for v in e:\n", " deg[int(v)] += 1\n", " return deg\n", "\n", "def degree_matrix(hg, sizes=None, num_nodes: int | None = None):\n", " \"\"\"Return dict {s: degree_vector} for requested sizes.\"\"\"\n", " if sizes is None:\n", " sizes = sizes_present(hg)\n", " if num_nodes is None:\n", " # If you used 0..num_nodes-1 in generation, this works well\n", " num_nodes = int(nodes_present(hg).max()) + 1\n", " return {s: degree_by_size(hg, s, num_nodes=num_nodes) for s in sizes}\n", "\n", "def spearman_corr_matrix(vectors_by_size: dict[int, np.ndarray]):\n", " \"\"\"Compute Spearman correlation matrix between degree vectors across sizes.\"\"\"\n", " sizes = sorted(vectors_by_size.keys())\n", " M = np.zeros((len(sizes), len(sizes)), dtype=float)\n", " for i, si in enumerate(sizes):\n", " for j, sj in enumerate(sizes):\n", " if i == j:\n", " M[i, j] = 1.0\n", " else:\n", " M[i, j], _ = spearmanr(vectors_by_size[si], vectors_by_size[sj])\n", " return sizes, M" ], "id": "5abc8c51" }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "# -----------------------------\n", "# Plotting utilities\n", "# -----------------------------\n", "\n", "def plot_corr_matrix(sizes, M, title=\"Spearman correlation across size-layers\", vmin=-1.0, vmax=1.0, cmap=\"coolwarm\"):\n", " \"\"\"Plot a matrix with a diverging colormap and fixed bounds (useful for correlations).\"\"\"\n", " plt.figure()\n", " im = plt.imshow(M, interpolation=\"nearest\", vmin=vmin, vmax=vmax, cmap=cmap)\n", " plt.colorbar(im)\n", " plt.xticks(range(len(sizes)), sizes)\n", " plt.yticks(range(len(sizes)), sizes)\n", " plt.title(title)\n", " plt.xlabel(\"layer size s\")\n", " plt.ylabel(\"layer size s\")\n", " plt.tight_layout()\n", " plt.show()\n", "\n", "def plot_degree_ccdf(deg, label=None):\n", " \"\"\"CCDF P(K >= k) plotted on log-log axes.\"\"\"\n", " deg = np.asarray(deg)\n", " deg = deg[deg > 0]\n", " if deg.size == 0:\n", " return\n", " vals = np.sort(deg)\n", " # unique k and ccdf\n", " k = np.unique(vals)\n", " ccdf = np.array([(vals >= kk).mean() for kk in k])\n", " plt.loglog(k, ccdf, marker=\"o\", linestyle=\"none\", label=label)\n", "\n", "def plot_degree_distributions(degrees_by_size: dict[int, np.ndarray], title=\"Degree CCDF by size-layer\"):\n", " plt.figure()\n", " for s, deg in sorted(degrees_by_size.items()):\n", " plot_degree_ccdf(deg, label=f\"s={s}\")\n", " plt.xlabel(\"k\")\n", " plt.ylabel(\"P(K \u2265 k)\")\n", " plt.title(title)\n", " plt.legend()\n", " plt.show()\n", "\n", "def plot_rank_scatter(deg_a, deg_b, a_label=\"layer A\", b_label=\"layer B\"):\n", " \"\"\"Scatter of node degree ranks (Spearman visualization).\"\"\"\n", " ra = np.argsort(np.argsort(deg_a)) # 0..n-1 ranks\n", " rb = np.argsort(np.argsort(deg_b))\n", " plt.figure()\n", " plt.scatter(ra, rb, s=8, alpha=0.4)\n", " plt.xlabel(f\"rank({a_label})\")\n", " plt.ylabel(f\"rank({b_label})\")\n", " corr, _ = spearmanr(deg_a, deg_b)\n", " plt.title(f\"Rank\u2013rank scatter (Spearman={corr:.3f})\")\n", " plt.show()\n" ], "id": "3e921440" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1) Generate a baseline hypergraph\n", "\n", "We generate a multi-layer hypergraph with sizes s=2,3,4.\n", "Use enough hyperedges per layer for stable degree correlations; parameters are described below.\n" ], "id": "f10f6647" }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sizes present: [2, 3, 4]\n", "s=2: edges=4000\n", "s=3: edges=2500\n", "s=4: edges=1500\n" ] } ], "source": [ "num_nodes = 500\n", "edges_by_size = {2: 4000, 3: 2500, 4: 1500}\n", "\n", "alpha_by_size = 1.1 # stronger hubs with larger alpha\n", "rho = 0.8 # strong correlation across layers\n", "seed = 7\n", "\n", "H = scale_free_hypergraph(\n", " num_nodes=num_nodes,\n", " edges_by_size=edges_by_size,\n", " alpha_by_size=alpha_by_size,\n", " rho=rho,\n", " seed=seed,\n", " enforce_unique_edges=True,\n", ")\n", "\n", "print(\"sizes present:\", sizes_present(H))\n", "for s in sorted(edges_by_size):\n", " print(f\"s={s}: edges={len(edges_of_size(H, s))}\")\n" ], "id": "ce6594b6" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2) Size-specific degrees and inter-layer correlation\n", "\n", "We compute \\(k_i^{(s)}\\) for each layer and visualize:\n", "\n", "- **Spearman correlation matrix** across layers (degree vectors),\n", "- a **rank\u2013rank scatter** between two chosen layers.\n" ], "id": "e8dda34f" }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Spearman correlations of realized degrees:\n", " s=2 vs s=3: 0.570\n", " s=2 vs s=4: 0.577\n", " s=3 vs s=4: 0.538\n" ] }, { "data": { "image/png": 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rVD+tOzHVM3sHVajQCDlStBbgObUK99pA5KcMsawzWXLbHpF/0++iE6rqRKN9h9zqlFXPqsyY6nd1R6qGejrhqB42WY224t3uBTFoUrTtr+2sdihTpkyJ+h41ThTtW7qTU4ZEy2q+jj+d9HXRzu0uPiffffedu8tUlkKBYmS5RG0rIi+2kqhur9rOao+j9gxqw6K7a7VHUHCvebntZwrgFbjo3OO1u4ksvwaBy2nwN61bAZ2XLQndLrr4KcumO2W1u1G51IZBx7naGBx//PG+vqfKo+2shsTReMFKcRDPuSMv0c5TsfzO3g1kLNcZ3bypPZluoBScK2Oi85g6GihIRv4UWEd5ryGU0rDRItNQakinVsTeXYBaXCutpxRkbnSS0l2usi6hFwc/wU68klUGNbxUo968Gv/qbkoHYGj2QxkZ7+/xfL4u1LrT8Hti1MGqLJJO2KF3rwo+8nuR976LTgra/h5l33SxyGvfiZU+R9tT+62XQfIaq+nOKZ5tmtN2VvZQgUVu20IXZmWQVLUZmk3Lq/orJ7qL9RoqPvnkk4dlz7yGvwquc9u23vaIdpzrt4qVMgua1FBRAaqCIjVSDq0eDaXfSMvoN9FdamSXZa/8ytDkVn5VbaoqIlRosKX1KPuhSd9RFzgFRroJ8ajBt46V0N9P5zjx7uC1HlWF5rWfajkdN8rGFET2w9suOrdEZhxyo3O1Lvyx/M6xnju8fUfbLzQAVDW2MkZeMBDL98nrd1b5Y73OiDJiqjLXpHOMjhXtm8oQ0u07f+Ju86GTXbS7Ry/tFpkWV4o4NPWqrlYvvfSSS2V5fdB196ILVrSLrdd/XbwoOvTz1QJZn5EsySqDtolXpRXJ+2y1aledsnoThR64alWuaF8p7fzSwabvqkg/8vfW68iqqFB6n07EOtA9OplEG8lUB3lkV9lodMLQnf7UqVPDyqOeRkqrej1o4qVtKqG9D8TLTCTqczyqF1cPCLWwjxYgqO46p/1O3ztaQBcLVVXoAqn9K1r9uurBdUJX76dobTG841JZLV2QVRUZ2u5EF3R1dc6LsheR+5d3BxvZ1TiU9ktdpBU4RatOVDszXZjU5VsX/ZzKr++ufSt00sVF1Vrq5RBK69MFLLJcP/74Y9hxqp4Taoei7+EFMvqddY5QmSNp/9dx6x332h7R7rATkS3VeVffQRmcyO+X2/q1/2mf0DGs3j4eVRlGfqdYzx26YVVXfO373vcX9TLMq1ra7+/s5zoTeW7TeUdNCVT2/LZLQgIyH+p2pgNTDayUAlZUqC5jugAqyo9sUKe6Re20oV1tJfTgUndXBTVqyKbGR/qhFfkraNFdjVcnqzpXZRz02boI6I532rRpbvloO15BSFYZVKWjLIu67CkNrYNM20F3vvo83bGpa6a6BqsaSONHaPvrPUol6+Kpk0x+6YBWKl6Rvtf9TevT99WJVp+t7m7RaLvoYq2urqorVV2q+vLrTiuyzYW+l35jLa+6bl1ItB9Eu3NRWbTfaL2q1tEdl/YnVfuFNi6Nh7ar0rKqF9ZFQQGcutPq4qptEJmij5dGoPzPf/7jggEdA6pXVtCm7JXm68Suk7QuGjoJqhpAXTW1r+mkrcxEZLYxL2o0q4ujTsb6PUJ/EwWt+p4KPNQNUuVTN291D9ZvoAuP3q9y/utf/3Lv0YVMv7m64Gpf1X7qjZOQ1zGh7arfUMeT9jk1htT30ud7gWC0Lp9qJKtqPe1boVkI0b6gTI6qYtQFU+XQeUltbhToaTtr/com5USBmbJRChp0bKuaSfu9MmDaFqF0d6+G6mqgqPYhGjdCy4UGhjqedezq/KHjVfu9Akt9Fx2zOsbU3kz7l7a5gmxlGbSvK8ujqkz9LXT00vzQ91Y1nTJKOm68sX10o6PzeuQYQaF07KkaQg1n1cXbu9HR9g3dh2I9d2h/VpddXVPUtkjbWsur4bPWEUtW1M/vHOt1Rseagkbt4/o9FWBpX9c+Hs85Ne0F4vT666+7LqXHHnus65qn7o9NmjQJXHHFFYFNmzaFLauPGzZsmOsKqu5QZcqUcd3P1G0qkt6rZevXrx8oVaqU6xbZuXPnwIMPPhhcRl2pbr31VtfNzFvXq6++elhXz5y6nYV2Ld2yZUvY/Jy6Taq7V2i3q0SUIa9ug56ffvopMHz48MARRxzhtrO6A+tzQruKabsNGjQoUKNGDbdMy5YtD+tSmZ/t4VEXwpNPPtltG0363fU7rVq1KmzbRXapfOSRR4K/ud6jMnmfFeqrr74KnHLKKa5Ls/7mdR+M7CIY2rVW69M+ou7Nl112mesWmdtvlls5o1G3v3/+85+uq54+R/vkmDFjAvv27TtsfX662ubUfU/dkCdNmuT+ru1VtWrVQNu2bV0Z1G3T8/LLLwdatWrlujs2aNDAvUddjCO3U15dbb1tG22K3D46VtWNUV0R9bmNGzcODBw4MKz7vLefNGvWzJW/efPmrot4LNt7xYoVrpv3UUcd5d5bq1Yt1+03cv2hx4zX7TKnKdRHH30UOOecc1yXTq1f5TnvvPMC8+fPz7VcOsa0n2tf02+s76/uqf/5z3/CltP6evXq5YYb0G/j7e/PPPPMYetU92XtRzpf6ljVMXviiScGJk+eHDZUgbrz61jVerRczZo1Az169AgsX7487q62ofuSPlvHnbrgt2/fPvDkk08G8rJo0SK3b6pc6vaqLuHRjutYzx0yderU4PlU5VD3cn1G9+7dg8t4v3m07ernd47lOjN9+nR3TvLWpX3+uuuuCzsW4V+G/i9ZgY4iVw1+5N0hAUBxomyjsrtqnIjEUKZHWTZV30SrjkTRxCD4AIBCQe1OIu+HVSWoKpDQ4dVR9PFYSABAoaDu1BpWXW3b1PhU7S/UiFzZJM1D8UHwAQAoNNVWGrNGDWy97sUayE2NQ3kCefGS1GoXpdNo7wGguFLvDNp7xBd8qBeQhgxQz0n9V72FIp+Qns4WL17sermpN6DaUUYbsiCSHgugXmre05OjPXFbPRC1/dW1XD2A1KuvINHmAwCAImLPnj1uCAAFC7FQl2Z1C1bXbD1+QCP1qmt16HgsGhpDjyPQ4Jiq6tL6NSRG6OMcEi2pvV0AAEBiKPOhsVI0dkpO9GwajcUTOpiaxqbRuEUap0WU6dA4L17NhHoYqfpLY67ooYMFoUi3+dAG0miCGuilIJ69AQAonHTfrEHoVP0Q+TiAZPTKUbVQogQihuMXVZHE8jDFvGgk3cgh5JXVUAZE9D00KKUGgfNoe+o9BTlaeJEOPhR4eA/aAgCkHz2iQ0+tTmbgUa9cRfvZ/u9xEfGqWLHiYaP/qgpEI77GS+1mNDJrKL3WsP96ZIOGrtcoytGW8Z4LVhCKdPDhDW37aEZDK59B85V01PGfiXmAHIqmQDa1xulq174D1mLizKQPca5MgQKPmSUaWvkENJvca9k2cPd3LojS8O+eRGQ9CrMiHXx4aSoFHuUzoj8yHcVbVlm636Uzgg+kqsq9QqkSCbnuZAQOmZIoCjxCg49E0XNp9GyhUHqtz9KTib0HukZbJvSJzolGugAAAJ8ySmZYZgKmjJIFGzx17NjR5s+fHzZPT5nWfNH4KXqwYegyak+p194yBYHgAwCAImL37t2uy6wmryut/q0nTIsajmpgNo+ekP2///3PRo0a5dpw6KnRekK2RpL1qJutnpujpxjrqb2XXXaZ69Ib+VT6RCrS1S4AAKRCRqlMy0hAW8MMn6NdfPjhh27MjtDAQQYMGOAGD9uwYUMwEJGGDRu6rrYKNu655x7XOPfhhx92PV48559/vm3ZssXGjh3rGqi2bt3adcONbISaSEV6nA+11q1cubI9ndmYNh9p6o+3/d8BhPRDm4/0tXPfATt63IO2Y8eOAmkrkdd154Uax1qFzPivO3uyD9nZW79K+vdINapdAABAUlHtAgCATxmlMiwjM/7GohnZ6TlAJsEHAAA+ud4qCQg+MtM0+KDaBQAAJBWZDwAAfKLaJT4EHwAA+JRZIsNNca/nUHoGH1S7AACApCLzAQCATxklMtwU93osPTMfBB8AAKSq2sXSM/ig2gUAACQVmQ8AAHxST5eE9HYJpGfmg+ADAACfMkpkuinu9Vh6Pp+IahcAAJBUZD4AAPCJBqfxIfgAAMCnjAxGOI0H1S4AACCpyHwAAOBTRonfql7iXk/A0hLBBwAAqRrhNEC1CwAAQIEj8wEAgE8ZmZluSsR60hHBBwAAqRrhNJNqFwAAgAJH5gMAgFQNMhZIz8wHwQcAAD5R7RIfql0AAEBSkfkAAMCnjIwE9XbJSM8cAMEHAAA+Ue0Sn/QMuQAAQMqQ+QAAIFW9XbLTM/NB8AEAgE9Uu8SHahcAAJBUZD4AAPCJZ7vEh+ADAACfqHaJT3qGXAAAIGXIfAAA4BOZj/gQfAAA4BPBR3yodgEAAElF8AEAQL4yH5kJmDJ8f/Z9991nDRo0sLJly1qHDh3sgw8+yHHZ0047zTIyMg6bevXqFVxm4MCBh/29e/fuVpCodgEAwCcFDYkY4TTjkL91PP300zZy5EibNm2aCzzuvvtu69atm61atcpq1ap12PLPP/+8HThwIPj6p59+suOOO87OPffcsOUUbDz66KPB12XKlLGCROYDAIAiYsqUKTZkyBAbNGiQNW/e3AUh5cuXtxkzZkRdvlq1alanTp3gNG/ePLd8ZPChYCN0uapVqxbo9yD4AAAgnw1OEzHJzp07w6b9+/dbJGUwli9fbl26dAnOy8zMdK+XLFlisXjkkUesb9++VqFChbD5b731lsucNG3a1C677DKXISlIBB8AAPiUmPYemcERTuvXr2+VK1cOThMnTjzsM7du3WqHDh2y2rVrh83X640bN+ZZZrUN+eyzz+ySSy45rMpl1qxZNn/+fJs0aZItWrTIevTo4T6roNDmAwCAFFu3bp1lZWUVaJsLZT1atmxp7du3D5uvTIhHf2/VqpU1btzYZUM6d+5sBYHMBwAAKa52ycrKCpuiBR81atSwEiVK2KZNm8Lm67XaaeRmz5499tRTT9ngwYPz/G6NGjVyn7V69WorKAQfAACkOPiIRenSpa1t27auesSTnZ3tXnfs2DHX9z7zzDOuHclFF12U5+f88MMPrs1H3bp1raAQfAAAUESMHDnSHnroIXvsscfsyy+/dI1DldVQ7xfp37+/jRkzJmqVy1lnnWXVq1cPm79792677rrr7P3337c1a9a4QKZ3797WpEkT14W3oNDmAwAAn0Ibi8a7Hj/OP/9827Jli40dO9Y1Mm3durXNmTMn2Ah17dq1rgdMKI0B8s4779jcuXMPW5+qcT755BMXzGzfvt3q1atnXbt2tfHjxxfoWB8EHwAAFKFnuwwfPtxN0aiRaCR1nw0EAlGXL1eunL3xxhuWbFS7AACApCLzAQBAEal2KS4IPgAA8Csj47cpEetJQ+kZcgEAgJQh8wEAgE/u0fOJaHCaQeYj6TR2/QknnGCVKlVyD7RRH2R1CQIAIJ2e7ZJuUvqt9fCaYcOGucFN9JjfgwcPuv7FGjAFAAAUTymtdtHAKKFmzpzpMiB6ZPApp5ySsnIBAFBYx/koDgpVm48dO3a4/1arVi3q3zUuvSbPzp07k1Y2AAA8dLWNT6H51no4zogRI+ykk06yFi1a5NhGpHLlysGpfv36SS8nAAAoJsGH2n589tln7pG/OdHDcpQd8aZ169YltYwAAEhGZqKebGtpqVBUu2iM+ldffdUWL15sRx55ZI7L6SE3BfmgGwAAYkGbjyIcfOhBN1dccYW98MIL7mE4DRs2TGVxAABAcQ8+VNXyxBNP2EsvveTG+tDjgUXtOfSkPQAACiU1FE1EY9HM9Kx3Sem3fuCBB1zbjdNOO83q1q0bnJ5++ulUFgsAgLxHOE3QlI5SXu0CAADSS6FocAoAQFHCOB/xIfgAAMAnervEJz1DLgAAkDJkPgAA8EujgyWiyiQjPXMABB8AAPiVoGoXo9oFAACg4JH5AADAp4yMTDclYj3piOADAID8VJdQ7ZJv6RlyAQCAlCHzAQCATwwyFh+CDwAAfGKQsfikZ8gFAABShswHAAB+6Wm0ieipkpGemQ+CDwAAfKLaJT5UuwAAgKQi8wEAgF/qpZKIniqZ6ZkDIPgAAMCnjIwMNyViPekoPUMuAACQMmQ+AADwSz1dElFlkpGeOQCCDwAAfKK3S3zSM+QCAAApQ/ABAEB+qksSNfl03333WYMGDaxs2bLWoUMH++CDD3JcdubMmcHGsd6k94UKBAI2duxYq1u3rpUrV866dOli33zzjRUkgg8AAPxSdUmiJh+efvppGzlypI0bN85WrFhhxx13nHXr1s02b96c43uysrJsw4YNwen7778P+/vtt99uU6dOtWnTptnSpUutQoUKbp379u2zgkLwAQBAETFlyhQbMmSIDRo0yJo3b+4ChvLly9uMGTNyfI+yHXXq1AlOtWvXDst63H333XbDDTdY7969rVWrVjZr1iz78ccf7cUXXyyw70HwAQCATxkZmQmbZOfOnWHT/v37LdKBAwds+fLlrlrEk5mZ6V4vWbLEcrJ79247+uijrX79+i7A+Pzzz4N/++6772zjxo1h66xcubKrzsltnfEi+AAAIMXVLvXr13cXfW+aOHHiYR+5detWO3ToUFjmQvRaAUQ0TZs2dVmRl156yR5//HHLzs62E0880X744Qf3d+99ftaZCHS1BQAgxdatW+faZnjKlCmTkPV27NjRTR4FHs2aNbPp06fb+PHjLVUIPgAA8CkjM9NNiViPKPAIDT6iqVGjhpUoUcI2bdoUNl+v1ZYjFqVKlbLjjz/eVq9e7V5779M61NsldJ2tW7e2gkK1CwAAfumZLImaYlS6dGlr27atzZ8/PzhP1Sh6HZrdyI2qbT799NNgoNGwYUMXgISuU21O1Osl1nXmB5kPAACKiJEjR9qAAQOsXbt21r59e9dTZc+ePa73i/Tv39+OOOKIYJuRm2++2f7whz9YkyZNbPv27XbHHXe4rraXXHJJsCfMiBEj7JZbbrFjjjnGBSM33nij1atXz84666wC+x4EHwAA+OUaiyag8iDT3zgf559/vm3ZssUNCqYGoaoamTNnTrDB6Nq1a10PGM/PP//suuZq2apVq7rMyXvvvee66XpGjRrlApihQ4e6AOXkk09264wcjCyRMgLq5FtEKTWkVsFPZza28hklUl0cpMAfb+uW6iIghQLZRfb0hTjt3HfAjh73oO3YsSPPthIFcd3Z8MAYyyoX/8V55y/7rO5lE5P+PVKNNh8AACCpqHYBACDFvV3SDcEHAAB+5fOhcFHXk4bS81sDAICUIfMBAIBfGp/DZ0+VHNeThgg+AADwKfShcPGuJx2l57cGAAApQ+YDAAC/Qp5IG/d60hDBBwAAftHbJS7p+a0BAEDKkPkAAMAvn0+kzXU9aYjgAwAAvzQyaUIeLJdp6Sg9vzUAAEgZMh8AAPhFg9O4EHwAAOAXXW3jkp4hFwAASBkyHwAA5Ku3SyKqXTIsHRF8AADgF11t40K1CwAASCoyHwAA+MU4H3Eh+AAAwC+qXeKSniEXAABIGTIfAAD4xSBjcSH4AAAgP0FDItprZKRn8JGe3xoAAKRMsch8dPxnF8sqWzrVxUAKvH39G6kuAlLo1ClnpLoISJESqS4ADU7jUiyCDwAAkoo2H3FJz28NAABShswHAAB+Ue0SF4IPAAD8YoTTuKTntwYAAClD5gMAAJ8CGRluSsR60hHBBwAA+WrzkYjeLhmWjqh2AQAASUXmAwAAvxjnIy4EHwAA+ESbj/ikZ8gFAABShuADAID8VrskYvLpvvvuswYNGljZsmWtQ4cO9sEHH+S47EMPPWR//OMfrWrVqm7q0qXLYcsPHDjQMjIywqbu3btbQSL4AAAgvyOcJmLy4emnn7aRI0fauHHjbMWKFXbcccdZt27dbPPmzVGXf+utt+yCCy6whQsX2pIlS6x+/frWtWtXW79+fdhyCjY2bNgQnJ588kkrSAQfAAAUEVOmTLEhQ4bYoEGDrHnz5jZt2jQrX768zZgxI+rys2fPtssvv9xat25txx57rD388MOWnZ1t8+fPD1uuTJkyVqdOneCkLElBIvgAACC/w6snYjKznTt3hk379+8/7CMPHDhgy5cvd1Un/1eMTPdaWY1Y7N271w4ePGjVqlU7LENSq1Yta9q0qV122WX2008/WUEi+AAAIJ+9XRIxiapDKleuHJwmTpxokbZu3WqHDh2y2rVrh83X640bN1osRo8ebfXq1QsLYFTlMmvWLJcNmTRpki1atMh69OjhPqug0NUWAIAUW7dunWVlZYVVgyTabbfdZk899ZTLcqixqqdv377Bf7ds2dJatWpljRs3dst17tzZCgKZDwAAUtzbJSsrK2yKFnzUqFHDSpQoYZs2bQqbr9dqp5GbyZMnu+Bj7ty5LrjITaNGjdxnrV692goKwQcAAD4FMjITNsWqdOnS1rZt27DGol7j0Y4dO+b4vttvv93Gjx9vc+bMsXbt2uX5OT/88INr81G3bl0rKAQfAAAUEepmq7E7HnvsMfvyyy9d49A9e/a43i/Sv39/GzNmTHB5teG48cYbXW8YjQ2itiGadu/e7f6u/1533XX2/vvv25o1a1wg07t3b2vSpInrwltQaPMBAIBf+RijI8f1+HD++efbli1bbOzYsS6IUBdaZTS8Rqhr1651PWA8DzzwgOsl85e//CVsPRon5KabbnLVOJ988okLZrZv3+4ao2ocEGVKCqLdiYfgAwAAnwLmr8okt/X4NXz4cDdFo0aioZTNyE25cuXsjTfesGSj2gUAACQVmQ8AAIpItUtxQfABAEC+go8EVB5kpGfwkZBqFzVSAQAAKJDgQ9129FQ9z3nnnWfVq1e3I444wj7++GO/qwMAwNJ9ePV04zv40BP0NAa9zJs3z02vv/66GwdefYUBACj2EjzCabrx3eZD/Yq94OPVV191mQ/1CdbgJR06dCiIMgIAgGLEd8hVtWpV9wAc0cAm3pPxAoFAgT4BDwCAwiJgGQmb0pHvzMc555xjF154oR1zzDFu7HdVt8hHH33khmMFAKC48/tcltzWk458Bx933XWXq2JR9kMPq6lYsaKbv2HDBrv88ssLoowAACCdg49SpUrZtddee9j8q6++OlFlAgCgcEtUY9EMMh8AACAGieomG6CrLQAAQMEj8wEAgE80OI1Pen5rAABQtIIPPcvl4YcftjFjxti2bdvcvBUrVtj69esTXT4AAArvU20TMaUh39Uun3zyiRtYrHLlyrZmzRobMmSIVatWzZ5//nlbu3atzZo1q2BKCgBAYZGgahej2iU2I0eOtIEDB9o333xjZcuWDc7v2bOnLV68ONHlAwAA6Z75WLZsmU2fPv2w+XqqrZ77AgBAcZeoodEDDK8emzJlytjOnTsPm//1119bzZo1E1UuAAAKLXq7xMf3tz7zzDPt5ptvtoMHD7rXGRkZrq3H6NGjrU+fPnEWBwAAFHe+g48777zTdu/ebbVq1bJffvnFTj31VPdAuUqVKtmECRMKppQAABQmqi1JSG8XS0u+q13Uy2XevHn2zjvvuJ4vCkTatGnjesAAAJAOApbppkSsJx35Dj5UxVK7dm07+eST3eQJBALuSbdHHXVUossIAACKEd8hV4MGDVym49tvvw2bv3nzZmvYsGEiywYAQKF+sFwipnSUr3xPs2bNrH379jZ//vyw+cp+AACQLr1dEjGlI9/fWr1b7r//frvhhhusV69eNnXq1LC/AQAAJLTNh5fduPrqq+3YY4+1Cy64wD799FMbO3as31UBAFAkMchYfHwHH6F69Ohh7733nhv744MPPoizKAAAFA0MMhYf399a43qULl06+Lp58+a2dOlSq1KlCm0+AABA4jMfCxcuPGxe9erVbdGiRX5XBQBAkZSoniqBNG0rGVPwoWe5ZGVlBf+dG285AACKK9p8JCH4qFq1qm3YsMENqa7qlWi9WlTlovmHDh2Ks0gAAMDSPfhYsGCBVatWLcdqFwAA0gkNTpMQfKiRabR/AwCQjqh2iY/vkGvOnDnuoXKe++67z1q3bm0XXnih/fzzz3EWBwAAFHe+g4/rrrsu2OhUg4uNHDnSevbsad999537NwAAafFU20QMr27pWe3i+1sryNDYHvLcc8/ZGWecYbfeeqvLgLz++uu+1vXAAw9Yq1atXA8ZTR07dvS9DgAAUlXtkojJL11v9ZDXsmXLWocOHfIc5POZZ55xI5Jr+ZYtW9prr712WIcRjVJet25dK1eunHXp0sW++eYbK1TBhwYY27t3r/v3m2++aV27dnX/VoPUvLrhRjryyCPttttus+XLl9uHH35onTp1st69e9vnn3/ut1gAABR7Tz/9tKtlGDdunK1YscKOO+4469atm3uyfDQahVyPQRk8eLB99NFHdtZZZ7nps88+Cy5z++23u+e0TZs2zQ0aWqFCBbfOffv2FZ7g4+STT3ZffPz48S7a0sPl5Ouvv3bBhB/KmqjK5phjjrHf/e53NmHCBKtYsaK9//77fosFAECSBxlLRNVLhq/PnTJlig0ZMsQGDRrkaiEUMJQvX95mzJgRdfl77rnHunfv7ppM6In0una3adPG/vWvf/32PQIBu/vuu93DYnXzr9qIWbNm2Y8//mgvvviiFZrgQwUuWbKkPfvss67a5IgjjnDzVV2iL5hfGh/kqaeesj179rjqFwAACqtUVLscOHDA1RSoWsSTmZnpXi9ZsiTqezQ/dHlRVsNbXk0pNm7cGLZM5cqVXXVOTutMyfDqRx11lL366quHzb/rrrvyVQA1WlWwofSOsh4vvPBCsE1JpP3797vJ47eaBwCAwmhnxPWsTJkybgq1detWd6Neu3btsPl6/dVXX0VdrwKLaMtrvvd3b15OyxSElDezbdq0qa1cudLVM1122WU2YMAA++KLL6IuO3HiRBeReVP9+vWTXl4AALxnuyRiEl3PQq9vut4VZ74zH4mmBqxNmjRx/27btq0tW7bM1VFNnz79sGXHjBkT1p1XkSIBCAAg2QKBDDclYj2ybt26sGejRWY9pEaNGlaiRAnbtGlT2Hy9rlOnjkWj+bkt7/1X89TbJXQZjeFVbDMfkbKzs8OqVkLpx/C65XoTAABFXVbEtS1a8KGbdd2kz58/P+yaqdc5tZXU/NDlZd68ecHlGzZs6AKQ0GV0Y6/aiIJsf5nSzIcyGT169HDtSHbt2mVPPPGEvfXWW/bGG2+kslgAAOQhUQOEZfpaWtl/NU9o166dtW/f3vVUUUcN9X6R/v37u44gXrXNVVdd5R6Lcuedd7reqerYoaEtHnzwQfd3PRB2xIgRdsstt7iepwpGbrzxRqtXr57rklsogo+DBw+6AUjURqNFixZxf7j6JWtD6Ym5quNSFx8FHqeffnrc6wYAoLg92+X888+3LVu2uEHB1CBUVSN67InXYHTt2rWuB4znxBNPdDf26kr797//3QUY6kIbeg0fNWqUC2CGDh1q27dvd0NqaJ0alKygZATUydeHRo0auR4pGtgk1ZQaUtCydvzfLKts6VQXBynw9vVkydLZqVPOSHURkCI79+23I0f/y3bs2JHUKnjvurP8o8+sYqVKca9v965d1vb4Fkn/HqnmO2f0j3/8w0VP27ZtK5gSAQBQyKVyePXioGR+BhlbvXq1qw86+uij3TCsoTTcKwAAxVmqql3SNvgoyAYoAACg+PMdfOhhNgAApDMyH/HJVz8htYZ9+OGHXVdZr+2HqlvWr18fZ3EAACg6g4wlYkpHvjMfn3zyiXsAjVr7rlmzxj1dr1q1avb888+7Lj56Gh4AAEDCMh8a4GTgwIH2zTffhPUB7tmzpy1evNjv6gAAKHLo7ZLkzIeevRLtuSsaUa0gn4AHAEBhQZuPJGc+NN58tEfZf/3111azZs04iwMAAIo738HHmWeeaTfffLMbat0bF15tPUaPHm19+vQpiDICAFCoUO2S5OBDD6fZvXu31apVy3755Rf3wJomTZpYpUqVbMKECXEWBwCAws8FDono7WLpGXz4bvOhXi56HO8777zjer4oEGnTpo3rAQMAAJDw4ON///ufe7icnnqnCQCAdJNtGW5KxHrSke9qF1Wx/OlPf7LHH3/c9u3bVzClAgCgEKPNR5KDD41k2qpVKzfeR506dexvf/ubLV26NM5iAACAdOE7+GjdurXdc8899uOPP9qMGTNsw4YN9sc//tFatGhhU6ZMsS1bthRMSQEAKCQYXj0Fz3aRkiVL2jnnnGPPPPOMTZo0yVavXm3XXnut1a9f3/r37++CEgAAiqNAwqpe0lO+g48PP/zQLr/8cqtbt67LeCjw+Pbbb11PGGVFevfundiSAgCA9OztokDj0UcftVWrVrnnuehBcvpvZuZvcUzDhg1t5syZ1qBBg4IoLwAAKZeoKpNAmla7+A4+HnjgAbv44ovdw+WU9YhGA5A98sgjiSgfAACFDs92SXLwoafZ5qV06dI2YMCA/JYJAAAUY76DD8/evXvdM10OHDgQNl/dcAEAKM6odkly8KGutKpymTNnTtS/Hzp0KM4iAQBQuKmXSnaC1pOOfPd2GTFihO3YscMNLFauXDkXhDz22GN2zDHH2Msvv1wwpQQAAOmb+ViwYIG99NJL1q5dO9fD5eijj7bTTz/dsrKybOLEidarV6+CKSkAAIUE1S5Jznzs2bPH9WaRqlWrBkc0bdmypRt6HQCA4o5nuyQ5+GjatKkb40OOO+44mz59uq1fv96mTZuWY9dbAACAfFe7XHXVVcGh08eNG2fdu3e32bNnu+61GlwMAIDijmqXJAcfF110UfDfbdu2te+//96++uorO+qoo6xGjRpxFgcAgMKPQcZSNM6Hp3z58tamTZt4VwMAANJETMHHyJEjfT37BQCA4iw78NuUiPWko5iCj48++iimlWVkpGf6CACQXqh2SULwsXDhwjg/BgAAIEFtPgAASDf0dokPwQcAAD4FAr9NiVhPOvI9yBgAAEA8yHwAAOBTtmW4KRHrSUdkPgAAyGebj0RMBWXbtm3Wr18/9+DXKlWq2ODBg2337t25Ln/FFVe4x6joqfUaPPTKK690T7KP7NkaOT311FO+ykbmAwCAYqhfv37ucSjz5s2zgwcP2qBBg2zo0KH2xBNPRF3+xx9/dNPkyZOtefPmbgTzSy+91M179tlnw5Z99NFH3eNVPApu/CD4AACgmDU4/fLLL23OnDm2bNkya9eunZt37733Ws+ePV1wUa9evcPe06JFC3vuueeCrxs3bmwTJkxwj1X59ddfrWTJkmHBRp06dfJdPqpdAADI5yBjiZgKwpIlS1yA4AUe0qVLF8vMzLSlS5fGvB5VuajaJjTwkGHDhrnnubVv395mzJhhAZ9RFJkPAABSbOfOnWGvy5Qp46b82rhxo9WqVStsngKIatWqub/FYuvWrTZ+/HhXVRPq5ptvtk6dOrlnu82dO9cuv/xy15ZE7UNiReYDAIB8PtslEZPUr1/fKleuHJwmTpxo0Vx//fVRG3yGTnrSfCKCoV69erm2HzfddFPY32688UY76aST7Pjjj7fRo0fbqFGj7I477vC1fjIfAAD4laieKoHf1rFu3TpXveHJKetxzTXX2MCBA3NdZaNGjVx7jM2bN4fNV7sN9WjJq63Grl27XGPSSpUq2QsvvGClSpXKdfkOHTq4DMn+/ftjztYQfAAAkGJZWVlhwUdOatas6aa8dOzY0bZv327Lly+3tm3bunkLFiyw7OxsFyzklvHo1q2bCyJefvllK1u2bJ6ftXLlSqtataqvaiKCDwAAillvl2bNmrnsxZAhQ2zatGmuq+3w4cOtb9++wZ4u69evt86dO9usWbNcw1EFHl27drW9e/fa448/7l57bVEU8JQoUcJeeeUV27Rpk/3hD39wgYm68d5666127bXX+iofwQcAAMVwhNPZs2e7gEMBhnq59OnTx6ZOnRr8uwKSVatWuWBDVqxYEewJ06RJk7B1fffdd9agQQNXBXPffffZ1Vdf7Xq4aLkpU6a4IMcPgg8AAIqhatWq5TigmCiYCO0ie9ppp+XZZVbZlNDBxfKL4AMAgGJW7VLYEXwAAOBTop7LEijAZ7sUZozzAQAAkorMBwAAPoUOEBbvetIRwQcAAD7R5iM+VLsAAICkIvMBAIBPiXoibaAAx/kozAg+AADwKTtB7TWyLT1R7QIAAJKqWGQ+AtkBNyH9nDrljFQXASm0aOQrqS4CUmRv4FBKP58Gp/EpFsEHAADJRPARH6pdAABAUpH5AADAp+xAhpsSsZ50RPABAIBPVLvEh2oXAACQVGQ+AADwicxHfAg+AADIR9CQiBEeAmkafFDtAgAAkorMBwAAPgUCGW5KxHrSEcEHAAA+0eYjPlS7AACApCLzAQCAT2psmpCn2gYsLRF8AADgE9Uu8aHaBQAAJBWZDwAAfCLzER+CDwAAfKLNR3yodgEAAElF5gMAAJ+odokPwQcAAD5lZ/82JWI96YhqFwAAkFRkPgAA8Ilql/gQfAAA4BPBR3yodgEAAElF5gMAAJ/UTjQh43xYeiL4AADAp0Ag4KZErCcdUe0CAACSiswHAAA+0eA0PmQ+AADwKfD/BxmLdwoUYKOPbdu2Wb9+/SwrK8uqVKligwcPtt27d+f6ntNOO80yMjLCpksvvTRsmbVr11qvXr2sfPnyVqtWLbvuuuvs119/9VU2Mh8AABRD/fr1sw0bNti8efPs4MGDNmjQIBs6dKg98cQTub5vyJAhdvPNNwdfK8jwHDp0yAUederUsffee8+tv3///laqVCm79dZbYy4bwQcAAMWs2uXLL7+0OXPm2LJly6xdu3Zu3r333ms9e/a0yZMnW7169XJ8r4INBRfRzJ0717744gt78803rXbt2ta6dWsbP368jR492m666SYrXbp0TOWj2gUAAJ/UzTZRU0FYsmSJq2rxAg/p0qWLZWZm2tKlS3N97+zZs61GjRrWokULGzNmjO3duzdsvS1btnSBh6dbt262c+dO+/zzz2MuH5kPAABSbOfOnWGvy5Qp46b82rhxo2uPEapkyZJWrVo197ecXHjhhXb00Ue7zMgnn3ziMhqrVq2y559/Prje0MBDvNe5rTcSwQcAACmudqlfv37Y/HHjxrlqjEjXX3+9TZo0Kc8ql/xSmxCPMhx169a1zp0727fffmuNGze2RCH4AADAp0B2wE2JWI+sW7fO9Urx5JT1uOaaa2zgwIGWm0aNGrk2G5s3bw6brx4p6gGTU3uOaDp06OD+u3r1ahd86L0ffPBB2DKbNm1y//WzXoIPAABSLCsrKyz4yEnNmjXdlJeOHTva9u3bbfny5da2bVs3b8GCBZadnR0MKGKxcuVK919lQLz1TpgwwQU2XrWOetOo7M2bN495vTQ4BQCgmDU4bdasmXXv3t11m1Wm4t1337Xhw4db3759gz1d1q9fb8cee2wwk6GqFfVcUcCyZs0ae/nll1032lNOOcVatWrllunatasLMv7617/axx9/bG+88YbdcMMNNmzYMF9tVAg+AADIZ5uPREwFRb1WFFyozYa62J588sn24IMPBv+usT/UmNTrzaJusupCqwBD71MVT58+feyVV14JvqdEiRL26quvuv8qC3LRRRe5ACV0XJBYUO0CAEAxVK1atVwHFGvQoEHYg+3U6HXRokV5rle9YV577bW4ykbwAQCAT9nZATclYj3piOADAIBiNsJpYUebDwAAkFRkPgAA8InMR3wIPgAA8Ck7EHBTItaTjqh2AQAASUXmAwAAnwLZv02JWE86IvgAAMCngP6XgCqTgFHtAgAAUODIfAAAkI/qkmyqXfKN4AMAAJ9U5ZKQapcA1S4AAAAFjswHAAA+6ZEsiXgsS3Z6Jj4IPgAA8CuQHXBTItaTjqh2AQAASUXmAwAAn3i2S3wIPgAA8Ck7O+CmRKwnHVHtAgAAkorMBwAAPjHOR3wIPgAA8IkHy8WHahcAAJCewcdtt91mGRkZNmLEiFQXBQCAXGUHAgmb0lGhqHZZtmyZTZ8+3Vq1apXqogAAkCfafBTxzMfu3butX79+9tBDD1nVqlVTXRwAAFDcg49hw4ZZr169rEuXLqkuCgAAvsb5SMSUjlJa7fLUU0/ZihUrXLVLLPbv3+8mz86dOwuwdAAARMcIp0U087Fu3Tq76qqrbPbs2Va2bNmY3jNx4kSrXLlycKpfv36BlxMAABST4GP58uW2efNma9OmjZUsWdJNixYtsqlTp7p/Hzp06LD3jBkzxnbs2BGcFMAAAJCSBqfZCZgC6Zn6SFm1S+fOne3TTz8Nmzdo0CA79thjbfTo0VaiRInD3lOmTBk3AQCQSoEEdZMNEHwkV6VKlaxFixZh8ypUqGDVq1c/bD4AACg+CsU4HwAAFCVetUki1pOOClXw8dZbb6W6CAAA5Ingo4iP8wEAANJLocp8AABQFChhkYikRXZ6Jj4IPgAA8Itql/hQ7QIAAJKKzAcAAD7xVNv4kPkAAMCn7OxEPVzOCsy2bdvcU+OzsrKsSpUqNnjwYPck+ZysWbPGMjIyok7PPPNMcLlof9ez2vwg8wEAQDHUr18/27Bhg82bN88OHjzoRhEfOnSoPfHEE1GX1/PStHyoBx980O644w7r0aNH2PxHH33UunfvHnyt4MYPgg8AAIpZtcuXX35pc+bMcU+Nb9eunZt37733Ws+ePW3y5MlWr169w96jx5rUqVMnbN4LL7xg5513nlWsWDFsvoKNyGX9oNoFAACfEvJQuezE9JiJZsmSJS5A8AIP6dKli2VmZtrSpUtjfgDsypUrXXVNpGHDhlmNGjWsffv2NmPGDN9BFJkPAABSbOfOnQl9kOrGjRutVq1aYfP0xPhq1aq5v8XikUcesWbNmtmJJ54YNv/mm2+2Tp06Wfny5W3u3Ll2+eWXu7YkV155ZczlI/MBAECKMx/169e3ypUrB6eJEydG/dzrr78+x0ah3vTVV1/F/f1++eUX1zYkWtbjxhtvtJNOOsmOP/549xT6UaNGuXYhfpD5AADAp2wLWHYC2mtk22/rWLduneuV4skp63HNNdfYwIEDc11no0aNXHuMzZs3h83/9ddfXQ+YWNpqPPvss7Z3717r379/nst26NDBxo8fb/v37485W0PwAQBAimVlZYUFHzmpWbOmm/LSsWNH2759u2u30bZtWzdvwYIFlp2d7YKFWKpczjzzzJg+S+1Cqlat6quaiOADAIBiNrx6s2bNXFfYIUOG2LRp01xX2+HDh1vfvn2DPV3Wr19vnTt3tlmzZrmGo57Vq1fb4sWL7bXXXjtsva+88opt2rTJ/vCHP1jZsmVdN95bb73Vrr32Wl/lI/gAAKCYdbWV2bNnu4BDAYZ6ufTp08emTp1qHgUkq1atctUrodR75cgjj7SuXbtapFKlStl9991nV199tSt7kyZNbMqUKS7I8YPgAwCAYqhatWo5DigmDRo0iBr8KJOhKRplU0IHF8svgg8AAPJRXaLh0ROxnnRE8AEAQDFr81HYMc4HAABIKjIfAAAUwwanhRnBBwAAPgWys92UiPWkI6pdAABAUpH5AADAp+wE9XbJTtMGpwQfAAD4RJuP+FDtAgAAkorMBwAAPjHOR3wIPgAA8IngIz5UuwAAgKQi8wEAgE/Z+l8gOyHrSUcEHwAA+KS4IzHVLpaWqHYBAABJReYDAACfaHAaH4IPAAB8YpCx+FDtAgAAkorMBwAAPmVnZ7spEetJRwQfAAD4RJuP+FDtAgAAkorMBwAAPgUC2W5KxHrSEcEHAAA+Ue0SH6pdAABAUpH5AADArwRlPixNMx8EHwAA+KSHyiXkwXKB9GzzQbULAABIKjIfAAD4RIPT+BB8AACQn662CRidNEC1CwAAQMEj8wEAgE9Uu8SH4AMAAJ8Y4TQ+VLsAAICkIvMBAIBPamuanYAqk+z0THwQfAAA4Jd6uiSkt0t2ekYfVLsAAICkIvMBAIBP9HaJD5kPAADy2dslEVNBmTBhgp144olWvnx5q1KlSkzvCQQCNnbsWKtbt66VK1fOunTpYt98803YMtu2bbN+/fpZVlaWW+/gwYNt9+7dvspG8AEAQDF04MABO/fcc+2yyy6L+T233367TZ061aZNm2ZLly61ChUqWLdu3Wzfvn3BZRR4fP755zZv3jx79dVXbfHixTZ06FBfZaPaBQCAYljt8s9//tP9d+bMmbGVJRCwu+++22644Qbr3bu3mzdr1iyrXbu2vfjii9a3b1/78ssvbc6cObZs2TJr166dW+bee++1nj172uTJk61evXoxfRaZDwAA8tnbJRFTYfHdd9/Zxo0bXVWLp3LlytahQwdbsmSJe63/qqrFCzxEy2dmZrpMSVpkPhSlya59B1JdFKRIiVQXACm1N3Ao1UVAiuz9/20lvOtAsh36dU9C17Nz586w+WXKlHFTMinwEGU6Qum19zf9t1atWmF/L1mypFWrVi24TLEPPnbt2uX+22JibCklAEDxouuA7s6TpXTp0lanTh37cP55CVtnxYoVrX79+mHzxo0bZzfddNNhy15//fU2adKkXNenqpFjjz3WCrMiHXyobmndunVWqVIly8jIsHSjSFk7rLaBWh0jvfD7p7d0//2V8VDgEWsbg0QpW7asq55QY85EfpeMiGtYTlmPa665xgYOHJjr+ho1apSvciiokk2bNrneLh69bt26dXCZzZs3h73v119/dT1gvPcX++BDdUxHHnmkpTudeNLx5IPf8Punt3T+/ZOZ8YgMQDSlQs2aNd1UEBo2bOgCiPnz5weDDQW5asvh9Zjp2LGjbd++3ZYvX25t27Z18xYsWGDZ2dmubUisaHAKAEAxtHbtWlu5cqX776FDh9y/NYWOyaHqmRdeeMH9W9mXESNG2C233GIvv/yyffrpp9a/f3+XXTrrrLPcMs2aNbPu3bvbkCFD7IMPPrB3333Xhg8f7nrC+MlCFenMBwAAiE6DhT322GPB18cff7z778KFC+20005z/161apXt2LEjuMyoUaNsz549btwOZThOPvlk17U2NNMze/ZsF3B07tzZ1UD06dPHjQ3iR0YgVU2FEbf9+/fbxIkTbcyYMUlvFY3U4/dPb/z+KMoIPgAAQFLR5gMAACQVwQcAAEgqgg8AAJBUBB9FkBqZnXDCCW5wNQ1zqy5QarGM9PDAAw9Yq1atguM7qN/966+/nupiIUVuu+22YBdJoKgg+CiCFi1aZMOGDbP333/fPdL44MGD1rVrV9c9CsWfBtbTBUeD/Hz44YfWqVMn9wRKPeIa6UVPFp0+fboLRoGihN4uxcCWLVtcBkRBySmnnJLq4iAF9FCnO+64wwYPHpzqoiBJNFBUmzZt7P7773eDQmlESj0OHSgKyHwUA94AMboAIb1o1MKnnnrKZb1U/YL0oexnr169wh5/DhQVjHBaxGk8fdX1nnTSSdaiRYtUFwdJomGPFWzs27fPPRFTwyM3b9481cVCkijgXLFihat2AYoigo9icPfz2Wef2TvvvJPqoiCJmjZt6p7RoKzXs88+awMGDHDVbgQgxZ+eYnvVVVe59l6pergZEC/afBRhGlv/pZdessWLF7unESJ9KfXeuHFj1/gQxduLL75oZ599tpUoUSKs+k09XvScDQ27Hvo3oDAi81EEKV684oorXKr9rbfeIvCAq37TRQfFnx7mpWq3UIMGDXJPJx09ejSBB4oEgo8iWtXyxBNPuKyHxvrYuHGjm1+5cmUrV65cqouHAqYHifXo0cOOOuoo27Vrl9sXFIS+8cYbqS4akkDHfGT7rgoVKlj16tVp94Uig+CjiA4yJd4jkT2PPvqoDRw4MEWlQrJs3rzZ+vfvbxs2bHABp8Z4UOBx+umnp7poABAT2nwAAICkYpwPAACQVAQfAAAgqQg+AABAUhF8AACApCL4AAAASUXwAQAAkorgAwAAJBXBBwAASCqCDyAGGk12xIgRVtRo2HU9cGz79u2pLgoABBF8AMXYiSeeGByGHQAKC4IPoIg4cOCA7/eULl3a6tSp47IfAFBYEHwA+fDvf//b2rVr554wqov7hRde6B74JnpcUpMmTWzy5Mlh71m5cqULAlavXu1eqyrkkksusZo1a1pWVpZ16tTJPv744+DyN910k7Vu3doefvhha9iwoZUtWzZqWb7//ns744wzrGrVqu7ppr///e/ttddei1rtouojvY6c1qxZE1OZogVEw4cPt7p167ryHX300TZx4sS4ty+A4o3gA8iHgwcP2vjx492F+cUXX3QXb++JwrqYX3zxxe4pw6H0+pRTTnGBiZx77rkuYHn99ddt+fLl1qZNG+vcubNt27Yt+B4FKs8995w9//zzLniJZtiwYbZ//35bvHixffrppzZp0iSrWLFi1GW1HlXDeNM555xjTZs2tdq1a8dcplBTp061l19+2f7zn//YqlWrbPbs2dagQYN8blUAaUNPtQWQu1NPPTVw1VVX5fj3ZcuW6enQgV27drnX69evD5QoUSKwdOlS9/rAgQOBGjVqBGbOnOlev/3224GsrKzAvn37wtbTuHHjwPTp092/x40bFyhVqlRg8+bNuZatZcuWgZtuuinq3xYuXOjK9fPPPx/2tylTpgSqVKkSWLVqVcxlinTFFVcEOnXqFMjOzs61jAAQiswHkA/KCqiq46ijjnJVL6eeeqqbv3btWvffevXqWa9evWzGjBnu9SuvvOKyE8osiDImu3fvturVq7sshTd999139u233wY/R9UYqgLJzZVXXmm33HKLnXTSSTZu3Dj75JNP8iy/MhvXX3+9Pf300/a73/3OV5lCKdujjIyyJyrH3LlzY96GANJXyVQXAChq9uzZY926dXOTqhkUHCjo0OvQRqFqO/HXv/7V7rrrLlflcv7551v58uXd33SRVzsJtcmIVKVKleC/1YYjL/ocffZ///tfd/FXm4s777zTrrjiiqjLf/HFF9a3b1+77bbbrGvXrsH5sZYplKplFJwomHnzzTftvPPOsy5dutizzz6bZ7kBpC+CD8Cnr776yn766Sd38a5fv76b9+GHHx62XM+ePV3w8MADD9icOXNcm4zQi/bGjRutZMmSCWkjoXJceumlbhozZow99NBDUYOPrVu3uoxNnz597Oqrrw77W37LpIapCqw0/eUvf7Hu3bu7NiLVqlWL+3sBKJ4IPgCfVNWiLqz33nuvu9h/9tlnrvFppBIlSrhqCQUDxxxzjHXs2DH4N2UH9Pqss86y22+/3VV9/Pjjjy57cfbZZ7ueNLHS4Gc9evRw6/j5559t4cKF1qxZs6jLKuhQ9kU9aRRoeJS9yU+ZpkyZ4rIlxx9/vGVmZtozzzzjev/klCkBAKHNB+CTLtQzZ850F9rmzZu7DEhkt1rP4MGDXVXMoEGDwuarR4y6w6r3i/6mC72qQtRt1ut5EqtDhw65Hi8KOJR10Lruv//+qMsq+6JgSW1JFDR407p16/JVJrV3UaCiwOSEE05wvX60DgUiAJCTDLU6zfGvAOLy9ttvu66qurj7DSoAoLgi+AAKgHq2bNmyxQYMGOCqIdQwFQDwG3KjQAF48sknXdWGRgxVtQQA4P+Q+QAAAElF5gMAACQVwQcAAEgqgg8AAJBUBB8AACCpCD4AAEBSEXwAAICkIvgAAABJRfABAACSiuADAABYMv0/3zuFlGk5y80AAAAASUVORK5CYII=", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "deg = degree_matrix(H, sizes=sorted(edges_by_size.keys()), num_nodes=num_nodes)\n", "sizes, M = spearman_corr_matrix(deg)\n", "\n", "print(\"Spearman correlations of realized degrees:\")\n", "for i, si in enumerate(sizes):\n", " for j, sj in enumerate(sizes):\n", " if j > i:\n", " print(f\" s={si} vs s={sj}: {M[i,j]:.3f}\")\n", "\n", "plot_corr_matrix(sizes, M, title=\"Spearman correlation of realized size-specific degrees\")\n", "plot_rank_scatter(deg[2], deg[3], a_label=\"s=2\", b_label=\"s=3\")\n" ], "id": "de1aab42" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3) Degree distributions across layers\n", "\n", "A common visualization for heavy-tailed degree distributions is the **CCDF** on log\u2013log axes.\n", "If the generator is behaving as expected, you should see:\n", "\n", "- broad/heavy-tailed degree distributions in each layer,\n", "- heavier tails (more extreme hubs) when `alpha_by_size` is larger.\n" ], "id": "ae5863da" }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_degree_distributions(deg, title=\"Degree CCDF by size-layer (baseline)\")\n" ], "id": "d4e2777d" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4) Generating a variety of hypergraphs\n", "\n", "Below we vary:\n", "\n", "- **hub persistence** (`rho`): independent layers (`rho\u22480`), aligned hubs (`rho>0`), anti-aligned hubs (`rho<0`);\n", "- **heterogeneity** (`alpha_by_size`): weaker hubs vs stronger hubs;\n", "- **layer-specific heterogeneity**: different `alpha` for each layer.\n", "\n", "We track:\n", "- inter-layer Spearman correlations of realized degrees,\n", "- CCDFs per layer.\n" ], "id": "d0e0ec76" }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Case A: Independent layers (rho=0.0)\n", " alpha_by_size: 1.1 rho: 0.0\n", " Spearman(k^(s=2), k^(s=3)) = 0.016\n", " Spearman(k^(s=2), k^(s=4)) = -0.016\n", " Spearman(k^(s=3), k^(s=4)) = -0.033\n" ] }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Case B: Strongly aligned hubs (rho=0.85)\n", " alpha_by_size: 1.1 rho: 0.85\n", " Spearman(k^(s=2), k^(s=3)) = 0.643\n", " Spearman(k^(s=2), k^(s=4)) = 0.629\n", " Spearman(k^(s=3), k^(s=4)) = 0.590\n" ] }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Case C: Anti-aligned hubs (rho=-0.35)\n", " alpha_by_size: 1.1 rho: -0.35\n", " Spearman(k^(s=2), k^(s=3)) = -0.269\n", " Spearman(k^(s=2), k^(s=4)) = -0.268\n", " Spearman(k^(s=3), k^(s=4)) = -0.181\n" ] }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Case D: Layer-dependent heterogeneity (alpha varies by size)\n", " alpha_by_size: {2: 0.8, 3: 1.1, 4: 1.4} rho: 0.75\n", " Spearman(k^(s=2), k^(s=3)) = 0.556\n", " Spearman(k^(s=2), k^(s=4)) = 0.505\n", " Spearman(k^(s=3), k^(s=4)) = 0.504\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def summarize_hypergraph(num_nodes, edges_by_size, alpha_by_size, rho, seed=0):\n", " H = scale_free_hypergraph(\n", " num_nodes=num_nodes,\n", " edges_by_size=edges_by_size,\n", " alpha_by_size=alpha_by_size,\n", " rho=rho,\n", " seed=seed,\n", " enforce_unique_edges=True,\n", " )\n", " deg = degree_matrix(H, sizes=sorted(edges_by_size), num_nodes=num_nodes)\n", " sizes, M = spearman_corr_matrix(deg)\n", " return H, deg, sizes, M\n", "\n", "def show_case(title, num_nodes, edges_by_size, alpha_by_size, rho, seed=0):\n", " H, deg, sizes, M = summarize_hypergraph(num_nodes, edges_by_size, alpha_by_size, rho, seed=seed)\n", " print(title)\n", " print(\" alpha_by_size:\", alpha_by_size, \" rho:\", rho)\n", " for i, si in enumerate(sizes):\n", " for j, sj in enumerate(sizes):\n", " if j > i:\n", " print(f\" Spearman(k^(s={si}), k^(s={sj})) = {M[i,j]:.3f}\")\n", " plot_corr_matrix(sizes, M, title=f\"{title} \u2014 Spearman(degrees)\")\n", " plot_degree_distributions(deg, title=f\"{title} \u2014 degree CCDFs\")\n", " return H, deg, sizes, M\n", "\n", "num_nodes = 600\n", "edges_by_size = {2: 6000, 3: 3500, 4: 2000}\n", "seed = 11\n", "\n", "# 4.1 Independent layers (rho ~ 0)\n", "_ = show_case(\n", " title=\"Case A: Independent layers (rho=0.0)\",\n", " num_nodes=num_nodes,\n", " edges_by_size=edges_by_size,\n", " alpha_by_size=1.1,\n", " rho=0.0,\n", " seed=seed,\n", ")\n", "\n", "# 4.2 Strongly aligned hubs (rho > 0)\n", "_ = show_case(\n", " title=\"Case B: Strongly aligned hubs (rho=0.85)\",\n", " num_nodes=num_nodes,\n", " edges_by_size=edges_by_size,\n", " alpha_by_size=1.1,\n", " rho=0.85,\n", " seed=seed,\n", ")\n", "\n", "# 4.3 Anti-aligned hubs (rho < 0) within feasibility bound:\n", "# With 3 layers, rho >= -1/(3-1) = -0.5\n", "_ = show_case(\n", " title=\"Case C: Anti-aligned hubs (rho=-0.35)\",\n", " num_nodes=num_nodes,\n", " edges_by_size=edges_by_size,\n", " alpha_by_size=1.1,\n", " rho=-0.35,\n", " seed=seed,\n", ")\n", "\n", "# 4.4 Layer-dependent heterogeneity (different alpha per layer)\n", "_ = show_case(\n", " title=\"Case D: Layer-dependent heterogeneity (alpha varies by size)\",\n", " num_nodes=num_nodes,\n", " edges_by_size=edges_by_size,\n", " alpha_by_size={2: 0.8, 3: 1.1, 4: 1.4},\n", " rho=0.75,\n", " seed=seed,\n", ")\n" ], "id": "4f5375c5" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5) Hub overlap across layers (optional visualization)\n", "\n", "Another intuitive diagnostic is how much the **top-q% hubs** overlap across layers.\n", "\n", "We compute, for each pair of layers, the Jaccard similarity between the sets of top hubs\n", "(according to size-specific degree).\n" ], "id": "a690d600" }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def top_hubs(deg, q=0.05):\n", " n = len(deg)\n", " k = max(1, int(round(q * n)))\n", " return set(np.argsort(deg)[-k:])\n", "\n", "def hub_overlap_matrix(deg_by_size: dict[int, np.ndarray], q=0.05):\n", " sizes = sorted(deg_by_size.keys())\n", " M = np.zeros((len(sizes), len(sizes)), dtype=float)\n", " tops = {s: top_hubs(deg_by_size[s], q=q) for s in sizes}\n", " for i, si in enumerate(sizes):\n", " for j, sj in enumerate(sizes):\n", " A, B = tops[si], tops[sj]\n", " M[i, j] = len(A & B) / len(A | B)\n", " return sizes, M\n", "\n", "# Using the last case generated above (Case D) if variables exist; otherwise recompute quickly.\n", "try:\n", " deg_last = deg\n", "except NameError:\n", " H_tmp = scale_free_hypergraph(\n", " num_nodes=600, edges_by_size={2: 6000, 3: 3500, 4: 2000},\n", " alpha_by_size=1.1, rho=0.75, seed=0\n", " )\n", " deg_last = degree_matrix(H_tmp, sizes=[2,3,4], num_nodes=600)\n", "\n", "sizes_h, J = hub_overlap_matrix(deg_last, q=0.05)\n", "plot_corr_matrix(sizes_h, J, title=\"Top-5% hub overlap (Jaccard) across layers\", vmin=0.0, vmax=1.0, cmap=\"viridis\")\n" ], "id": "a97cb9c3" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Notes / troubleshooting\n", "\n", "- If your realized degree correlations look noisy, increase `edges_by_size` (more hyperedges per layer).\n", "- Very large `alpha` can produce extremely dominant hubs (almost a star-like structure).\n", "- Negative `rho` is constrained when you have many sizes because the **equicorrelation matrix**\n", " must be a valid covariance/correlation matrix (PSD). With `m` sizes, the bound is \\(\\rho \\ge -1/(m-1)\\).\n" ], "id": "68d0d5f2" } ], "metadata": { "kernelspec": { "display_name": "hgx-installation", "language": "python", "name": "python3" }, "language_info": { "name": "python", "version": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 5 }